Question: Simplify the following expression: $z = \dfrac{8r^2 + 8r - 336}{r - 6} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $8$ , so we can rewrite the expression: $ z =\dfrac{8(r^2 + 1r - 42)}{r - 6} $ Then we factor the remaining polynomial: $r^2 + {1}r {-42} $ ${-6} + {7} = {1}$ ${-6} \times {7} = {-42}$ $ (r {-6}) (r + {7}) $ This gives us a factored expression: $\dfrac{8(r {-6}) (r + {7})}{r - 6}$ We can divide the numerator and denominator by $(r + 6)$ on condition that $r \neq 6$ Therefore $z = 8(r + 7); r \neq 6$